A difficult question. Firstly, average bond enthalpies are calculated using a wide variety of molecules in the gas phase. They don't really give any useful information over which isomer is more stable than another. The two compounds you mentioned have exactly the same number and type of bonds, but in different places. Mean bond enthalpy data would give the same value for both.
We can do direct experiments on each compound and measure the enthalpy of hydrogenation. In this case, you will find that cyclohexa-1,3-diene is slightly more stable than cyclohexa-1,4-diene. The 1,3-diene has the two double bonds separated by a single C-C bond - this is called 'conjugation'. All conjugated dienes are stabilized through delocalization of the electrons. In the 1,4 diene the C=C are too far apart for this to occur.